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Mathematics
Problem
8. Factorise each of the following: (i)
8
a
3
+
b
3
+
12
a
2
b
+
6
a
b
2
8 a^{3}+b^{3}+12 a^{2} b+6 a b^{2}
8
a
3
+
b
3
+
12
a
2
b
+
6
a
b
2
(ii)
8
a
3
−
b
3
−
12
a
2
b
+
6
a
b
2
8 a^{3}-b^{3}-12 a^{2} b+6 a b^{2}
8
a
3
−
b
3
−
12
a
2
b
+
6
a
b
2
(iii)
27
−
125
a
3
−
135
a
+
225
a
2
27-125 a^{3}-135 a+225 a^{2}
27
−
125
a
3
−
135
a
+
225
a
2
(iv)
64
a
3
−
27
b
3
−
144
a
2
b
+
108
a
b
2
64 a^{3}-27 b^{3}-144 a^{2} b+108 a b^{2}
64
a
3
−
27
b
3
−
144
a
2
b
+
108
a
b
2
(v)
27
p
3
−
1
216
−
9
2
p
2
+
1
4
p
27 p^{3}-\frac{1}{216}-\frac{9}{2} p^{2}+\frac{1}{4} p
27
p
3
−
216
1
−
2
9
p
2
+
4
1
p
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